Vector Algebra Question 297
Question: If a, b, c, d be the position vectors of the points A, B, C and D respectively referred to same origin O such that no three of these points are collinear and $ \mathbf{a}+\mathbf{c}=\mathbf{b}+\mathbf{d}, $ then quadrilateral ABCD is a
Options:
A) Square
B) Rhombus
C) Rectangle
D) Parallelogram
Show Answer
Answer:
Correct Answer: D
Solution:
- Given $ \mathbf{a}+\mathbf{c}=\mathbf{b}+\mathbf{d}\Rightarrow \frac{1}{2}(\mathbf{a}+\mathbf{c})=\frac{1}{2}(\mathbf{b}+\mathbf{d}) $ Here, mid points of $ \overrightarrow{AC} $ and $ \overrightarrow{BD} $ coincide, where $ \overrightarrow{AC} $ and $ \overrightarrow{BD} $ are diagonals. In addition, we know that diagonals of a parallelogram bisect each other. Hence quadrilateral is parallelogram.
BETA
